Jurnal Ilmiah Soulmath : Jurnal Edukasi Pendidikan Matematika
Vol 4 No 5 (2016)

Dimensi Matriks Dan Dimensi Partisi Pada Graf Hasil Operasi Korona




Article Info

Publish Date
18 Jul 2017

Abstract

Let????(????,????)is a connected graph.For an ordered set ????={????1,????2,…,????????} of vertices, ????⊆????(????), and a vertex ????∈????(????), the representation of ???? with respect to ???? is the ordered k-tuple ????(????|????)={????(????,????1),????(????,????2),…,????(????,????????)|∀????∈????(????)}. The set W is called a resolving set of G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called a basis for ????. The metric dimension of ????, denoted by ????????????(????), is the number of vertices in a basis of ????. Then, for a subset S of V(G), the distance between u and S is ????(????,????)=????????????{????(????,????)|∀????∈????,∀????∈????(????)}. Let Π=(????1,????2,…,????????)be an ordered l-partition of V(G), for∀????????⊂????(????) dan????∈????(????), the representation of v with respect to Π is the l-vector ????(????|Π)=(????(????,????1),????(????,????2),…,????(????,????????)). The set Π is called a resolving partition for G if the ????−vector ????(????|Π),∀????∈????(????)are distinct. The minimum l for which there is a resolving l-partition of V(G) is the partition dimension of G, denoted by ????????(????). In this paper, we determine the metric dimension and the partition dimension of corona product graphs ????????⨀????????−1, and we get some result that the metric dimension and partition dimension of ????????⨀????????−1respectively is????(????−2) and 2????−1, for????≥3.Keyword: Metric dimention, partition dimenstion,corona product graphs

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Journal Info

Abbrev

mipa

Publisher

Subject

Education Mathematics

Description

urnal SOULMATH berisi tulisan yang berasal dari hasil penelitian, kajian, atau karya ilmiah di bidang Pendidikan Matematika. Terbit dua kali setahun yaitu Maret dan Oktober. Artikel yang masuk akan direview oleh reviewer yang berkompeten di ...